Question

The angular frequency of a spring block system is ${\omega }_0$ This system is suspended from the ceiling of anelevator moving downwards with a constant speed v${}_0$. The block is at rest relative to the elevator. Lift issuddenly stopped. Assuming the downwards as a positive direction, choose the wrong statement:

• A. The amplitude of the block is $\frac{v_0}{{\omega }_0}$
• B. The initial phase of the block is $\pi$
• C. The equation of motion for the block is $\frac{v_0}{{\omega }_0}\sin {\omega }_0$t.
• D. The maximum speed of the block is v${}_0$.

Answer 1

The correct option is B The initial phase of the block is $\pi$

Since $V_0$ is the maximum speed of the ball in its equilibrium position.

$\therefore V_0={\omega }_{0}AA=\frac{V_0}{{\omega }_0}$

So equation of motion becomes $\frac{V_0}{{\omega }_0}=Asin{\omega }_{0}t$ as there was no initial phase in the SHM.

There was no initial phase in the SHM.

Hence B is correct.